You can use any kind of fabric you like for the applique, it doesn't have to be wool felt. The beauty of wool felt is that it doesn't fray so you can do raw edge applique with no fraying at all. If you used a cotton raw edge (with fusible) you may get a little bit of fray around the edges of the elements. You can also add a seam allowance to the applique and make it turned, if using a 100% cotton fabric. It is a cute quilt.
A great way to get a lot of small pieces of felted wool is to buy a scrap bag:
https://www.primitivegatherings.us/s...crap-bags.html
https://www.etsy.com/search?q=wool+felt+fabric+scrap
https://www.ericas.com/fabric/scrapbags_wool_felt.htm
If you are really lucky you may be able to find a white wool blazer or suit at a thrift store to felt yourself and dye (like PP suggested above). But I have had cases when the label said 100% wool and dry clean only the wool didn't felt for me with washing and drying.